🧮 algebra

1. **Problem statement:** We are given a quadrilateral with sides labeled as $20\sqrt{35}$, $15\sqrt{45}$, $72$, and $30\sqrt{5}$, and an internal segment labeled $2$. We need to s

1. Masalah: Diketahui jumlah siswa dari 3 kelas adalah 100, dengan kelas A = 25 siswa, selisih jumlah siswa kelas B dan C adalah 5, dan kelas C lebih banyak dari kelas B. Nilai rat

1. The problem is to simplify the expression $7 \times \left(\frac{1000}{600}\right)^3$. 2. First, simplify the fraction inside the parentheses: $\frac{1000}{600} = \frac{10}{6} =

1. **State the problem:** Solve the equation $x(x+a) = ab$ for $x$. 2. **Expand the left side:**

1. Stating the problem: Solve for $x$ in the equation $1440 = 7 \times \left( \frac{1000}{600} \right)^3$. 2. Simplify the fraction inside the parentheses:

1. The problem is to expand the expression for $i$ (assuming $i$ is the imaginary unit where $i^2 = -1$) or to expand a given expression involving $i$. Since the user did not speci

1. **State the problem:** Solve the simultaneous equations: $$3x + 4y = 29$$

1. Problem statement: Factor the quadratic expression $v^2 - 2v - 24$. 2. Goal: Find two numbers that multiply to $-24$ and add to $-2$.

1. Problem 2: Find the next number in the sequence 98, 96, 92, 86, 78, 68, 56, ______. 2. First, find the differences between consecutive terms:

1. State the problem: Factor and solve the quadratic equation $v^2 - 2v - 24 = 0$. 2. We look for two integers whose product is -24 and whose sum is -2.

1. The problem is to solve the quadratic equation $v^2 - 2v - 24 = 0$ for $v$. 2. We start by identifying the coefficients: $a = 1$, $b = -2$, and $c = -24$.

1. The problem is to solve for $y$ in the equation $$y^2 = 81$$. 2. To solve for $y$, take the square root of both sides. Remember that taking the square root gives two solutions,

1. The problem states that the minimum point of a function is at $(-4,-4)$. 2. This means the function reaches its lowest value at $x = -4$, and the function value there is $-4$.

1. **Problem Statement:** Given the graph of the function $y = f(x)$, answer the following questions based on the graph. 2. **(a) Evaluate $f(-2)$ and $f(6)$:**

1. **State the problem:** We need to find how many solutions the equation $$-4 - 16m - 2 = -16m - 6$$ has. 2. **Simplify both sides:** Combine like terms on the left side:

1. **State the problem:** Solve for $r$ in the equation $$20r = -5(13r - 17)$$. 2. **Distribute the right side:** Multiply $-5$ by each term inside the parentheses:

1. **State the problem:** Solve for $r$ in the equation $$20r = -5(13r - 17)$$. 2. **Distribute the right side:** Multiply $-5$ by each term inside the parentheses:

1. **State the problem:** Solve for $y$ in the equation $$3.4 + 5.1(y + 8) = 85.$$\n\n2. **Distribute 5.1:** Multiply 5.1 by both $y$ and 8:\n$$3.4 + 5.1y + 5.1 \times 8 = 85.$$\n\

1. The **range** of a function is the set of all possible output values (or $y$-values) that the function can produce. 2. To find the range on a graph, you look at the vertical spr

1. **State the problem:** Solve for $j$ in the equation $$-4j - 6(8 - 3j) = 8.$$\n\n2. **Distribute the $-6$ across the parentheses:**\n$$-4j - 6 \times 8 + 6 \times 3j = 8$$\n$$-4

1. **State the problem:** Simplify the expressions $2p - 1 - 3p - \frac{1}{4}$ and $4p - 1 + y - 1$.\n\n2. **Simplify the first expression:** Combine like terms involving $p$ and c